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In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique…

Econometrics · Economics 2026-04-22 Ruijun Bu , Degui Li , Oliver Linton , Hanchao Wang

In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, and their asymptotic properties are…

Statistical Finance · Quantitative Finance 2013-03-26 Yingying Li , Zhiyuan Zhang , Xinghua Zheng

We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process. The proposed test is based on high-frequency data and is robust to market microstructure frictions. For the test, local…

Statistics Theory · Mathematics 2018-06-12 Markus Bibinger , Lars Winkelmann

Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods…

Econometrics · Economics 2023-02-20 Qiang Liu , Zhi Liu

The high-frequency cross-correlation existing between pairs of stocks traded in a financial market are investigated in a set of 100 stocks traded in US equity markets. A hierarchical organization of the investigated stocks is obtained by…

Statistical Mechanics · Physics 2008-12-02 Giovanni Bonanno , Fabrizio Lillo , Rosario N. Mantegna

Our main task is to study the effect of corporate governance on the market liquidity of listed companies' stocks. We establish a theoretical model that contains the heterogeneity of investors' beliefs to explain the mechanisms by which…

Trading and Market Microstructure · Quantitative Finance 2020-01-20 Jianhao Su

This research presents a comprehensive framework for analyzing liquidity in financial markets, particularly in the context of high-frequency trading. By leveraging advanced machine learning classification techniques, including Logistic…

Trading and Market Microstructure · Quantitative Finance 2024-08-20 Sid Bhatia , Sidharth Peri , Sam Friedman , Michelle Malen

We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an It\^o semimartingale with jumps and general…

Statistics Theory · Mathematics 2024-11-20 Markus Bibinger

We consider the problem of testing the parametric form of the volatility for high frequency data. It is demonstrated that in the presence of microstructure noise commonly used tests do not keep the preassigned level and are inconsistent.…

Statistics Theory · Mathematics 2012-11-26 Mathias Vetter , Holger Dette

Using high-frequency time series of stock prices and share volumes sizes from January 2002-May 2009, this paper investigates whether the effects of the onset of high-frequency trading, most prominent since 2005, are apparent in the dynamics…

Trading and Market Microstructure · Quantitative Finance 2010-09-22 Reginald D. Smith

We propose a new estimator of high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure from noisy and asynchronous high-frequency data collected for an ultra-large number of assets. The noise processes are…

Econometrics · Economics 2024-03-12 Degui Li , Oliver Linton , Haoxuan Zhang

The paper tackles the problem of deriving a topological structure among stock prices from high frequency historical values. Similar studies using low frequency data have already provided valuable insights. However, in those cases data need…

Statistical Finance · Quantitative Finance 2008-12-02 Donatello Materassi , Giacomo Innocenti

We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…

Probability · Mathematics 2018-07-12 Łukasz Treszczotko

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self…

Trading and Market Microstructure · Quantitative Finance 2015-03-17 E. Bacry , S. Delattre , M. Hoffmann , J. F. Muzy

We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an…

Physics and Society · Physics 2009-11-13 Paweł Sieczka , Janusz A. Hołyst

We focus on estimating the integrated covariance of log-price processes in the presence of market microstructure noise. We construct an efficient unbiased estimator for the quadratic covariation of two It\^{o} processes in the case where…

Statistics Theory · Mathematics 2008-12-19 Markus Bibinger

Market Microstructure is the investigation of the process and protocols that govern the exchange of assets with the objective of reducing frictions that can impede the transfer. In financial markets, where there is an abundance of recorded…

Trading and Market Microstructure · Quantitative Finance 2017-03-28 Ravi Kashyap

The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a…

Statistics Theory · Mathematics 2010-01-25 Markus Reiß

This study examine the theoretical and empirical perspectives of the symmetric Hawkes model of the price tick structure. Combined with the maximum likelihood estimation, the model provides a proper method of volatility estimation…

Statistical Finance · Quantitative Finance 2019-08-15 Kyungsub Lee , Byoung Ki Seo

Using a recently developed method of noise level estimation that makes use of properties of the coarse grained-entropy we have analyzed the noise level for the Dow Jones index and a few stocks from the New York Stock Exchange. We have found…

Statistical Mechanics · Physics 2009-11-10 Krzysztof Urbanowicz , Janusz A. Holyst